Non-reciprocal light transport–
The reservoir-mediated interference demonstrated above allows the design of non-reciprocal light transport between Ch1 and Ch2 under appropriate reservoir parameters. For instance, we choose the parameters: \(\theta _{0}=0\) , \(\theta _{1}=0\) , and \(\theta _{2}=\pi \) ; and measure the EIT spectra by sweeping the applied magnetic field to vary the two-photon detuning as illustrated in Fig. REF (a). The inter-channel light transport is characterized by switching on the probe field of the input channel (such as Ch1/Ch2), and measuring the light intensity in the output channel (such as Ch2/Ch1) whose probe field is initially switched off. When Ch1 is set as the input channel (left panel of Fig. REF (a)), the EIT spectra in Ch2 has a transmission window near the two-photon resonance \(\delta _{B}=0\) , where \(T_{12}\propto {|e^{i\psi _p^{1\rightarrow 2}}+e^{i\psi _p^{0\rightarrow 2}}|^2}\propto 1+\cos (\theta _{0}-\theta _{1})=2\) , peaking under a constructive interference. By contrast, when Ch2 is the input channel (right panel of Fig. REF (a)), the EIT spectra in Ch1 becomes \(T_{21}\propto {|e^{i\psi _p^{2\rightarrow 1}}+e^{i\psi _p^{0\rightarrow 1}}|^2}\propto {1+\cos (\theta _{0}-\theta _{2})=0}\) , vanishing due to destructive interference.
The analysis here are consistent with our experimental observation in Fig. REF (b), where the directional light transport is clearly identified. The origin of the observed non-reciprocity is therefore the interference of spin waves along the path of the atomic motion, analogous to the time-modulation scheme [1]}.
The light transport can be easily tuned to be reciprocal, for instance, by setting \(\theta _0=\pi /4\) . For all our experiments here, the observed isolation is \(\sim \) 19 dB, and the un-transported power is absorbed by the atoms. In the Supplementary Material, we show that the non-reciprocity persists under a bi-directional input, where probes in both channels are switched on.
